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Non-associative algebraic structures: classification and structure

Ivan Kaygorodov

Abstract

These are detailed notes for a lecture on "Non-associative Algebraic Structures: Classification and Structure" which I presented as a part of my Agregação em Matemática e Applicações (University of Beira Interior, Covilhã, Portugal, 13-14/03/2023).

Non-associative algebraic structures: classification and structure

Abstract

These are detailed notes for a lecture on "Non-associative Algebraic Structures: Classification and Structure" which I presented as a part of my Agregação em Matemática e Applicações (University of Beira Interior, Covilhã, Portugal, 13-14/03/2023).
Paper Structure (32 sections, 77 equations)

This paper contains 32 sections, 77 equations.

Table of Contents

  1. Introduction
  2. Non-associative algebras
  3. Poisson algebras
  4. $n$-Ary algebras
  5. Classifications of non-associative algebras
  6. The algebraic classification of algebras
  7. The geometric classification of algebras
  8. Degenerations of algebras
  9. Conservative algebras and superalgebras
  10. Kantor product
  11. Universal conservative superalgebras
  12. Conservative algebras of $2$-dimensional algebras
  13. Non-associative algebras and superalgebras
  14. Leibniz algebras
  15. Anticommutative $\mathfrak{CD}$-algebras
  16. ...and 17 more sections

Theorems & Definitions (2)

  • Example 1
  • Example 2